| Elias Loomis - 1859 - 372 pages
...BxBC, or sin. A : sin. B : : BC : AC. THEOREM II. (50.) In any plane triangle, the sum of any two sides **is to their difference, as the tangent of half the sum of** the opposite angles is to the tangent of half their difference. Let ABC be any triangle ; then will... | |
| George Roberts Perkins - 1860 - 472 pages
...it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides **is to their difference as the tangent of half the sum of** the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : :... | |
| Euclides - 1860 - 288 pages
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle **is to their difference as the tangent of half the sum of** the angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B... | |
| War office - 1861 - 714 pages
...=2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides **is to their difference as the tangent of half the sum of** the angles at the base is to the tangent of half their difference. 6. Observers on two ships a mile... | |
| Benjamin Greenleaf - 1862 - 518 pages
...__ cot ^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two **angles is to their difference as the tangent of half the sum of** the angles is to the tangent of half their difference, or as the cotangent of half their difference... | |
| Benjamin Greenleaf - 1861 - 638 pages
...B _ cot ^ (A — B) tf"\ sin A — sin B ~~ coti (A + B) ' ( ' that is, The sum of the sines of two **angles is to their difference as the tangent of half the sum of** the angles is to the tangent of half their difference, or as the cotangent of half their difference... | |
| Benjamin Greenleaf - 1863 - 504 pages
...sin B _ cot | (A — B) . . sin "A ^^sin "B ~ cot ±1 (A^~B) ' that is, The sum of the sines of two **angles is to their difference as the tangent- of half the sum of** the angles is to the tangent of half their difference, or as the cotangent of half their difference... | |
| William Frothingham Bradbury - 1864 - 324 pages
...the first proportion in Theorem I. THEOREM III. 41. In any plane triangle, the sum of any two sides **is to their difference, as the tangent of half the sum of** the opposite angles is to the tangent of half their difference. Let ABC be a triangle ; then AB + BC:BC—... | |
| McGill University - 1865 - 332 pages
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle **is to their difference as the tangent of half the sum of** the base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds... | |
| Gerardus Beekman Docharty - 1867 - 474 pages
...sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides **is to their difference as the tangent of half the sum of** the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem... | |
| |